As a once almost neighborhood menace with a BB gun, I have no doubt it greatly helped my rifle shooting later on. Depending on the ambient light and head position on the stock you could often see the BB go, hit or miss. Either way it was very instructive. If he finds he can hit from the right despite left eye dominance, it may be the more practical route to keep him there.
That's what I'm thinking. I'm showing him a basic version of Instinct Shooting I was taught.
Here's a story about the method:
http://pointshooting.com/qk.pdfCheck it out.
With a 30 minute refresher, I can shoot dimes out of the air with regularity with a BB gun. Ping pong balls get to be no challenge. The guy who once taught me would shoot BB's out of the air. He couldn't do it every time, but he didn't ever practice either. That is impressive.